Simplify the following expression: $ t = \dfrac{-7}{4} + \dfrac{-3k}{-k - 9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-k - 9}{-k - 9}$ $ \dfrac{-7}{4} \times \dfrac{-k - 9}{-k - 9} = \dfrac{7k + 63}{-4k - 36} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-3k}{-k - 9} \times \dfrac{4}{4} = \dfrac{-12k}{-4k - 36} $ Therefore $ t = \dfrac{7k + 63}{-4k - 36} + \dfrac{-12k}{-4k - 36} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{7k + 63 - 12k}{-4k - 36} $ $t = \dfrac{-5k + 63}{-4k - 36}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{5k - 63}{4k + 36}$